You're getting a burn because you're using your muscles in a way they haven't been used before. If you continue with these 1/4 ROM lifts, the burn will subside as you adapt to the work.

However, non-full ROM lifts on certain exercises can cause extreme stress on affected joints/tendons and can lead to injuries. 1/4 squats would be a good example of this.

It's not 1/4 reps. It's 1 and 1/4 reps. For example, on squats you go atg, come out of the hole 1/4 of the way up, back down and up. That's 1 rep. That's what the OP is talking about except the guy was benching.

"I'm a street walking cheetah with a heart full of napalm." -Iggy and The Stooges

we used to use a method like this in powerlifting it was called a lockout, it was more of a central nervous system exercise but it is very stimulating to the muscle as well what I used to do is a bench press with 20-40% over my full range ability and do them for 10x2 and then go full range you feel allot stronger

the 1/4 is at the toughest part of the lift. so it's like doing 2x as many lifts at that point in the motion.

Muscle confusion. that makes sense too. the muscles probably are thinking, "ho hum, lift againg", and then, "wait, you can't stop and go back down, we are supposed to go up, we aren't reagy" - hence the screaming

What I got a kick out of is the second chance. when you come down on a squat or a bench, you are pretty confident you got it all, but what if you didn't? this gives you a chance to work through the form one more time, and get it right, before you do the full lift.

At my house, we listen to both kinds of music: Led and Zeppelin!
How do you build muscle like Bert Landry?